Fuzzy sets are an extension of classical sets, used to mathematically model indefinite concepts, such as that of customer satisfaction. This is obtained by introducing a membership function expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets represent an extension of the theory of fuzzy sets, in which also a suitable non-membership function is defined. In this paper we aim at quantifying a latent construct, namely satisfaction, using fuzzy sets and intuitionistic fuzzy sets. We put forth a general evaluation method: first, we introduce a fuzzy satisfaction index to obtain membership values. Second, inferential confidence intervals (ICI), calculated through Bootstrap-t and percentile procedures, are used to assess the uncertainty underpinning membership and non-membership estimates. Third, we address the problem of optimal and multiple ICI, as well as their generalization through p values and q-values. In particular, we consider the problem of analyzing the responses to evaluation questionnaires. We apply this new method to a national program of evaluation of University courses and we discuss our framework in comparison with other evaluation techniques.

Marasini, D., Quatto, P., Ripamonti, E. (2017). Inferential confidence intervals for fuzzy analysis of teaching satisfaction. QUALITY & QUANTITY, 51(4), 1513-1529 [10.1007/s11135-016-0349-7].

### Inferential confidence intervals for fuzzy analysis of teaching satisfaction

#### Abstract

Fuzzy sets are an extension of classical sets, used to mathematically model indefinite concepts, such as that of customer satisfaction. This is obtained by introducing a membership function expressing the degree of membership of the elements to a set. Intuitionistic fuzzy sets represent an extension of the theory of fuzzy sets, in which also a suitable non-membership function is defined. In this paper we aim at quantifying a latent construct, namely satisfaction, using fuzzy sets and intuitionistic fuzzy sets. We put forth a general evaluation method: first, we introduce a fuzzy satisfaction index to obtain membership values. Second, inferential confidence intervals (ICI), calculated through Bootstrap-t and percentile procedures, are used to assess the uncertainty underpinning membership and non-membership estimates. Third, we address the problem of optimal and multiple ICI, as well as their generalization through p values and q-values. In particular, we consider the problem of analyzing the responses to evaluation questionnaires. We apply this new method to a national program of evaluation of University courses and we discuss our framework in comparison with other evaluation techniques.
##### Scheda breve Scheda completa Scheda completa (DC) Articolo in rivista - Articolo scientifico
Bootstrap methods; Fuzzy sets; Inferential confidence intervals; Intuitionistic fuzzy sets; Positive false discovery rate; Satisfaction indices; Teaching evaluation;
Bootstrap methods; Fuzzy sets; Inferential confidence intervals; Intuitionistic fuzzy sets; Positive false discovery rate; Satisfaction indices; Teaching evaluation; Statistics and Probability; Social Sciences (all)
English
2017
51
4
1513
1529
reserved
Marasini, D., Quatto, P., Ripamonti, E. (2017). Inferential confidence intervals for fuzzy analysis of teaching satisfaction. QUALITY & QUANTITY, 51(4), 1513-1529 [10.1007/s11135-016-0349-7].
File in questo prodotto:
File
InferentialConfidenceIntervals.pdf

Solo gestori archivio

Tipologia di allegato: Publisher’s Version (Version of Record, VoR)
Dimensione 467.83 kB
Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10281/128111`
• 6
• 5